I'm stuck on this:
For all positive integers n and all integers a, gcf(a, a+n) | n.
(For all positive integers n and all integers a, the greatest common fact of 'a' and 'a+n' divides into 'n').
Anybody know where to start?
The "if and only if" is correct, but it's not a real definition ;-)
You can say "if c=ax+by, SO gcf(a,b) divides c"
Let's write it :-)
If d=gcf(a,b), then a=da' and b=db' (with a' and b' coprime, but it doesn't matter for the demonstration)
So c=da'x+b'dy=d(a'x+b'y)
So d divides c, it's as simple as this ^^